Avalanche-size distribution of Cayley tree

Area of Science:

• Network Science
• Complex Systems
• Information Security

Background:

• Network immunization strategies combat malicious phenomena like epidemics and fake news.
• Traditional methods evaluate attacks using macro parameters (e.g., giant component size).
• A micro-perspective analysis of individual node removals and their consequences is lacking.

Purpose of the Study:

• To introduce and apply a micro-scale analysis of network attacks focusing on node removal consequences.
• To analyze the phenomenon of 'avalanches' triggered by single node removals.
• To analytically derive the distribution of avalanche sizes during network immunization.

Main Methods:

• Network percolation theory.
• Analysis of single node removal impact on network fragmentation.
• Analytical derivation of avalanche size distribution for random attacks on Cayley tree networks.

Main Results:

• Identified 'avalanches' as a significant contributor to network fragmentation beyond the initial node removal.
• Quantified the size of avalanches, defined as nodes disconnected from the giant component.
• Derived the analytical distribution of avalanche sizes for random attacks on Cayley tree networks.

Conclusions:

• A micro-scale analysis of node removal avalanches provides deeper insights into network immunization effectiveness.
• Avalanche size distribution is a key parameter for understanding network fragmentation dynamics.
• The analytical framework developed can inform strategies for combating network-based threats.